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Abstract
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We study the Nordhaus-Gaddum type results for (k−1,k,j) and k-domination numbers of a graph G and investigate these bounds for the k-limited packing and k-total limited packing numbers in graphs with emphasis on the case k=1. In the special case (k−1,k,j)=(1,2,0), we give an upper bound on dd(G)+dd(¯¯¯¯G) stronger than the bound presented by Harary and Haynes (1996). Moreover, we establish upper bounds on the sum and product of packing and open packing numbers and characterize all graphs attaining these bounds.
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